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The network reciprocity is an important dynamic rule fostering the emergence of cooperation among selfish individuals. This was reported firstly in the seminal work of Nowak and May, where individuals were arranged on the regular lattice network, and played the prisoner's dilemma game (PDG). In the standard PDG, one often assumes that the players have perfect rationality. However, in reality, we human are far from rational agents, as we often make mistakes, and behave irrationally. Accordingly, in this work, we introduce the element of noise into the measurement of fitness, which is determined by the parameter a controlling the degree of noise. The considered noise-induced mechanism remarkably promotes the behavior of cooperation, which may be conducive to interpret the emergence of cooperation within the population., Comment: 13 pages, 6 figures, accepted by Chaos, Solitons & Fractals